Lines, Angles, & Triangles - PSAT Math
Card 1 of 30
What is the measure of each angle in an equilateral triangle?
What is the measure of each angle in an equilateral triangle?
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Each angle is $60^\circ$. All angles equal in an equilateral triangle: $180^\circ \div 3$.
Each angle is $60^\circ$. All angles equal in an equilateral triangle: $180^\circ \div 3$.
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What is the relationship between the base angles of an isosceles triangle?
What is the relationship between the base angles of an isosceles triangle?
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The base angles are congruent. Angles opposite equal sides are equal.
The base angles are congruent. Angles opposite equal sides are equal.
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What is the exterior angle theorem for a triangle?
What is the exterior angle theorem for a triangle?
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Exterior angle equals sum of two remote interior angles. Exterior angle extends one side beyond the triangle.
Exterior angle equals sum of two remote interior angles. Exterior angle extends one side beyond the triangle.
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What is the triangle inequality for side lengths $a$, $b$, and $c$?
What is the triangle inequality for side lengths $a$, $b$, and $c$?
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$a+b>c$, $a+c>b$, and $b+c>a$. Sum of any two sides must exceed the third side.
$a+b>c$, $a+c>b$, and $b+c>a$. Sum of any two sides must exceed the third side.
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What is the Pythagorean Theorem for a right triangle with legs $a$, $b$ and hypotenuse $c$?
What is the Pythagorean Theorem for a right triangle with legs $a$, $b$ and hypotenuse $c$?
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$a^2+b^2=c^2$. Relates legs and hypotenuse in right triangles.
$a^2+b^2=c^2$. Relates legs and hypotenuse in right triangles.
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What is the converse of the Pythagorean Theorem?
What is the converse of the Pythagorean Theorem?
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If $a^2+b^2=c^2$, then the triangle is right. Tests if a triangle is right-angled using side lengths.
If $a^2+b^2=c^2$, then the triangle is right. Tests if a triangle is right-angled using side lengths.
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What is the relationship between alternate interior angles when two parallel lines are cut by a transversal?
What is the relationship between alternate interior angles when two parallel lines are cut by a transversal?
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Alternate interior angles are congruent. Interior angles on opposite sides of transversal are equal.
Alternate interior angles are congruent. Interior angles on opposite sides of transversal are equal.
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What is the special right triangle ratio for a $45^\circ$-$45^\circ$-$90^\circ$ triangle?
What is the special right triangle ratio for a $45^\circ$-$45^\circ$-$90^\circ$ triangle?
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$x,x,x\sqrt{2}$. Isosceles right triangle: legs equal, hypotenuse is leg times $\sqrt{2}$.
$x,x,x\sqrt{2}$. Isosceles right triangle: legs equal, hypotenuse is leg times $\sqrt{2}$.
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What is the special right triangle ratio for a $30^\circ$-$60^\circ$-$90^\circ$ triangle?
What is the special right triangle ratio for a $30^\circ$-$60^\circ$-$90^\circ$ triangle?
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$x,x\sqrt{3},2x$. Sides opposite $30°$, $60°$, $90°$ angles respectively.
$x,x\sqrt{3},2x$. Sides opposite $30°$, $60°$, $90°$ angles respectively.
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What are the side ratios for a $45^\circ$-$45^\circ$-$90^\circ$ triangle?
What are the side ratios for a $45^\circ$-$45^\circ$-$90^\circ$ triangle?
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$1:1:\sqrt{2}$. Isosceles right triangle has legs equal and hypotenuse $\sqrt{2}$ times a leg.
$1:1:\sqrt{2}$. Isosceles right triangle has legs equal and hypotenuse $\sqrt{2}$ times a leg.
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What is the angle relationship called when two angles sum to $180^\circ$?
What is the angle relationship called when two angles sum to $180^\circ$?
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Supplementary angles. Two angles that add up to $180^\circ$ form a straight line together.
Supplementary angles. Two angles that add up to $180^\circ$ form a straight line together.
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Identify the missing angle: vertical to a $37^\circ$ angle is $ ^\circ$.
Identify the missing angle: vertical to a $37^\circ$ angle is $ ^\circ$.
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$37^\circ$. Vertical angles are congruent, so they have the same measure.
$37^\circ$. Vertical angles are congruent, so they have the same measure.
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What is the sum of the interior angles of a triangle in degrees?
What is the sum of the interior angles of a triangle in degrees?
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$180^\circ$. The angle sum property of triangles is always $180^\circ$.
$180^\circ$. The angle sum property of triangles is always $180^\circ$.
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Find the third angle of a triangle with angles $50^\circ$ and $60^\circ$.
Find the third angle of a triangle with angles $50^\circ$ and $60^\circ$.
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$70^\circ$. Use $180^\circ - 50^\circ - 60^\circ = 70^\circ$.
$70^\circ$. Use $180^\circ - 50^\circ - 60^\circ = 70^\circ$.
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What is the sum of the exterior angles of any polygon (one at each vertex)?
What is the sum of the exterior angles of any polygon (one at each vertex)?
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$360^\circ$. Each exterior angle pairs with an interior angle to make $180^\circ$.
$360^\circ$. Each exterior angle pairs with an interior angle to make $180^\circ$.
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What is the exterior angle measure if the interior angle is $125^\circ$?
What is the exterior angle measure if the interior angle is $125^\circ$?
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$55^\circ$. Exterior and interior angles are supplementary: $180^\circ - 125^\circ$.
$55^\circ$. Exterior and interior angles are supplementary: $180^\circ - 125^\circ$.
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What theorem states that an exterior angle of a triangle equals the sum of two remote interior angles?
What theorem states that an exterior angle of a triangle equals the sum of two remote interior angles?
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Exterior Angle Theorem. The exterior angle equals the sum of the two non-adjacent interior angles.
Exterior Angle Theorem. The exterior angle equals the sum of the two non-adjacent interior angles.
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In a triangle, what is the relationship between side length and opposite angle size?
In a triangle, what is the relationship between side length and opposite angle size?
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Longer side is opposite larger angle. In any triangle, larger angles are opposite longer sides.
Longer side is opposite larger angle. In any triangle, larger angles are opposite longer sides.
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What inequality must side lengths $a$, $b$, and $c$ satisfy to form a triangle?
What inequality must side lengths $a$, $b$, and $c$ satisfy to form a triangle?
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$a + b > c$, $a + c > b$, $b + c > a$. Triangle Inequality: sum of any two sides exceeds the third.
$a + b > c$, $a + c > b$, $b + c > a$. Triangle Inequality: sum of any two sides exceeds the third.
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Can lengths $3$, $4$, and $8$ form a triangle? Answer $\text{Yes}$ or $\text{No}$.
Can lengths $3$, $4$, and $8$ form a triangle? Answer $\text{Yes}$ or $\text{No}$.
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$\text{No}$. $3 + 4 = 7 < 8$, violating the triangle inequality.
$\text{No}$. $3 + 4 = 7 < 8$, violating the triangle inequality.
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Find $c$ if a right triangle has legs $5$ and $12$ and hypotenuse $c$.
Find $c$ if a right triangle has legs $5$ and $12$ and hypotenuse $c$.
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$13$. Apply Pythagorean theorem: $c = \sqrt{5^2 + 12^2} = \sqrt{169} = 13$.
$13$. Apply Pythagorean theorem: $c = \sqrt{5^2 + 12^2} = \sqrt{169} = 13$.
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What are the side ratios for a $30^\circ$-$60^\circ$-$90^\circ$ triangle?
What are the side ratios for a $30^\circ$-$60^\circ$-$90^\circ$ triangle?
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$1:\sqrt{3}:2$. Short leg : long leg : hypotenuse in a 30-60-90 triangle.
$1:\sqrt{3}:2$. Short leg : long leg : hypotenuse in a 30-60-90 triangle.
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If the short leg of a $30^\circ$-$60^\circ$-$90^\circ$ triangle is $7$, what is the hypotenuse?
If the short leg of a $30^\circ$-$60^\circ$-$90^\circ$ triangle is $7$, what is the hypotenuse?
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$14$. In 30-60-90 triangles, hypotenuse is twice the short leg.
$14$. In 30-60-90 triangles, hypotenuse is twice the short leg.
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What condition guarantees two triangles are similar using two pairs of equal angles?
What condition guarantees two triangles are similar using two pairs of equal angles?
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$\text{AA similarity}$. Two pairs of equal angles guarantee triangles are similar.
$\text{AA similarity}$. Two pairs of equal angles guarantee triangles are similar.
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What is the relationship between corresponding angles when two parallel lines are cut by a transversal?
What is the relationship between corresponding angles when two parallel lines are cut by a transversal?
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Corresponding angles are congruent. Same position angles at each intersection are equal.
Corresponding angles are congruent. Same position angles at each intersection are equal.
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What is the angle sum of a triangle in degrees?
What is the angle sum of a triangle in degrees?
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$180^\circ$. Sum of interior angles in any triangle is always $180^\circ$.
$180^\circ$. Sum of interior angles in any triangle is always $180^\circ$.
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What is the relationship between vertical angles formed by two intersecting lines?
What is the relationship between vertical angles formed by two intersecting lines?
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Vertical angles are congruent. Opposite angles formed by intersecting lines are equal.
Vertical angles are congruent. Opposite angles formed by intersecting lines are equal.
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If corresponding sides of similar triangles have ratio $\frac{3}{5}$, what is the ratio of their areas?
If corresponding sides of similar triangles have ratio $\frac{3}{5}$, what is the ratio of their areas?
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$\frac{9}{25}$. Area ratio equals the square of the side ratio: $(\frac{3}{5})^2$.
$\frac{9}{25}$. Area ratio equals the square of the side ratio: $(\frac{3}{5})^2$.
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What is the angle relationship called when two angles sum to $90^\circ$?
What is the angle relationship called when two angles sum to $90^\circ$?
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Complementary angles. Two angles that add up to $90^\circ$ form a right angle together.
Complementary angles. Two angles that add up to $90^\circ$ form a right angle together.
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What is the relationship between adjacent angles on a straight line?
What is the relationship between adjacent angles on a straight line?
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They are supplementary; sum is $180^\circ$. Adjacent angles on a line form a straight angle.
They are supplementary; sum is $180^\circ$. Adjacent angles on a line form a straight angle.
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